论文标题
3D轴向对称Prandtl方程的全局切向分析解
Global tangentially analytical solutions of the 3D axially symmetric Prandtl equations
论文作者
论文摘要
在本文中，我们将证明具有较小初始数据的三维轴向对称PrandTL边界层方程的全局解决方案，这在$ H^1 $ SOBOLEV空间相对于正常变量，并且相对于切向变量是分析性的。主要结果的证明依赖于构建切向加权的分析能量功能，该功能作用于特殊设计的好未知。构造的能量功能可以在Ignatova-Vicol [2016arma]中找到其二维平行的，其中没有引入切向重量，并且特殊的未知数设置为控制分析半径的下限，其二维相似性可以追溯到PAICU-ZHANG [202111MARMA]。我们的结果是在Ignatova-Vicol [2016arma]中的改善从几乎全球存在到全球存在，而Paicu-Zhang [2021MARMA]从两个维度的情况到轴向对称的三维情况。
In this paper, we will prove the global existence of solutions to the three dimensional axially symmetric Prandtl boundary layer equations with small initial data, which lies in $H^1$ Sobolev space with respect to the normal variable and is analytical with respect to the tangential variables. Proof of the main result relies on the construction of a tangentially weighted analytic energy functional, which acts on a specially designed good unknown. The constructed energy functional can find its two dimensional parallel in Ignatova-Vicol [2016ARMA] where no tangential weight is introduced and the specially good unknown is set to control the lower bound of the analytical radius, whose two dimensional similarity can be traced to Paicu-Zhang [2021ARMA]. Our result is an improvement of that in Ignatova-Vicol [2016ARMA] from the almost global existence to the global existence and an extension of that in Paicu-Zhang [2021ARMA] from the two dimensional case to the three dimensional axially symmetric case.
